





'''simple docstring'''






import re
from typing import Callable, List, Optional, Union

import tensorflow as tf


try:
					from tensorflow.keras.optimizers.legacy import Adam
except ImportError:
					from tensorflow.keras.optimizers import Adam
class 		lowerCamelCase	(   tf.keras.optimizers.schedules.LearningRateSchedule							):



	def __init__( self		,   a_		,   a_		,   a_		,   a_ = 1.0		,   a_ = None		,   ):
			super().__init__()
			lowerCAmelCase  :     List[Any]       						= initial_learning_rate
			lowerCAmelCase  :     Optional[int]       						= warmup_steps
			lowerCAmelCase  :     Dict       						= power
			lowerCAmelCase  :     str       						= decay_schedule_fn
			lowerCAmelCase  :     Optional[Any]       						= name



	def __call__( self		,   a_						):
			with tf.name_scope(self.name or "WarmUp"						) as name:
					# Implements polynomial warmup. i.e., if global_step < warmup_steps, the
					# learning rate will be `global_step/num_warmup_steps * init_lr`.
					lowerCAmelCase  :     int       						= tf.cast(a_		,   tf.floataa						)
					lowerCAmelCase  :     str       						= tf.cast(self.warmup_steps		,   tf.floataa						)
					lowerCAmelCase  :     Tuple       						= global_step_float / warmup_steps_float
					lowerCAmelCase  :     Tuple       						= self.initial_learning_rate * tf.math.pow(a_		,   self.power						)
					return tf.cond(
					    global_step_float < warmup_steps_float		,   lambda: warmup_learning_rate		,   lambda: self.decay_schedule_fn(step - self.warmup_steps						)		,   name=a_		,   )





	def 	_lowerCamelCase     ( self						):
			return {
			    "initial_learning_rate": self.initial_learning_rate,
			    "decay_schedule_fn": self.decay_schedule_fn,
			    "warmup_steps": self.warmup_steps,
			    "power": self.power,
			    "name": self.name,
			}






def   __A    (				a_    :	float   ,a_    :	int   ,a_    :	int   ,a_    :	float = 0.0   ,a_    :	float = 0.9   ,a_    :	float = 0.9_9_9   ,a_    :	float = 1e-8   ,a_    :	Optional[float] = None   ,a_    :	Optional[float] = None   ,a_    :	float = 0.0   ,a_    :	float = 1.0   ,a_    :	Optional[List[str]] = None   ,):
		lowerCAmelCase  :     Dict       						= tf.keras.optimizers.schedules.PolynomialDecay(
		    initial_learning_rate=a_   ,decay_steps=num_train_steps - num_warmup_steps   ,end_learning_rate=init_lr * min_lr_ratio   ,power=a_   ,)
		if num_warmup_steps:
				lowerCAmelCase  :     List[str]       						= WarmUp(
				    initial_learning_rate=a_   ,decay_schedule_fn=a_   ,warmup_steps=a_   ,)
		if weight_decay_rate > 0.0:
				lowerCAmelCase  :     Optional[int]       						= AdamWeightDecay(
				    learning_rate=a_   ,weight_decay_rate=a_   ,beta_a=a_   ,beta_a=a_   ,epsilon=a_   ,clipnorm=a_   ,global_clipnorm=a_   ,exclude_from_weight_decay=["LayerNorm", "layer_norm", "bias"]   ,include_in_weight_decay=a_   ,)
		else:
				lowerCAmelCase  :     Optional[Any]       						= tf.keras.optimizers.Adam(
				    learning_rate=a_   ,beta_a=a_   ,beta_a=a_   ,epsilon=a_   ,clipnorm=a_   ,global_clipnorm=a_   ,)
		# We return the optimizer and the LR scheduler in order to better track the
		# evolution of the LR independently of the optimizer.
		return optimizer, lr_schedule
class 		lowerCamelCase	(   _A							):



	def __init__( self		,   a_ = 0.001		,   a_ = 0.9		,   a_ = 0.999		,   a_ = 1e-7		,   a_ = False		,   a_ = 0.0		,   a_ = None		,   a_ = None		,   a_ = "AdamWeightDecay"		,   **a_		,   ):
			super().__init__(a_		,   a_		,   a_		,   a_		,   a_		,   a_		,   **a_						)
			lowerCAmelCase  :     int       						= weight_decay_rate
			lowerCAmelCase  :     Any       						= include_in_weight_decay
			lowerCAmelCase  :     Tuple       						= exclude_from_weight_decay



	@classmethod
	def 	_lowerCamelCase     ( cls		,   a_						):
			lowerCAmelCase  :     str       						= {"WarmUp": WarmUp}
			return super(a_		,   cls						).from_config(a_		,   custom_objects=a_						)



	def 	_lowerCamelCase     ( self		,   a_		,   a_		,   a_						):
			super(a_		,   self						)._prepare_local(a_		,   a_		,   a_						)
			lowerCAmelCase  :     Optional[Any]       						= tf.constant(
			    self.weight_decay_rate		,   name="adam_weight_decay_rate"						)



	def 	_lowerCamelCase     ( self		,   a_		,   a_		,   a_						):
			lowerCAmelCase  :     str       						= self._do_use_weight_decay(var.name						)
			if do_decay:
					return var.assign_sub(
					    learning_rate * var * apply_state[(var.device, var.dtype.base_dtype)]["weight_decay_rate"]		,   use_locking=self._use_locking		,   )
			return tf.no_op()



	def 	_lowerCamelCase     ( self		,   a_		,   a_=None		,   **a_						):
			lowerCAmelCase						,		lowerCAmelCase  :     str       						= list(zip(*a_						)						)
			return super(a_		,   self						).apply_gradients(zip(a_		,   a_						)		,   name=a_		,   **a_						)



	def 	_lowerCamelCase     ( self		,   a_		,   a_		,   a_						):
			if apply_state is None:
					return self._decayed_lr_t[var_dtype], {}

			lowerCAmelCase  :     Dict       						= apply_state or {}
			lowerCAmelCase  :     int       						= apply_state.get((var_device, var_dtype)						)
			if coefficients is None:
					lowerCAmelCase  :     Optional[Any]       						= self._fallback_apply_state(a_		,   a_						)
					lowerCAmelCase  :     Optional[int]       						= coefficients

			return coefficients["lr_t"], {"apply_state": apply_state}



	def 	_lowerCamelCase     ( self		,   a_		,   a_		,   a_=None						):
			lowerCAmelCase						,		lowerCAmelCase  :     Dict       						= self._get_lr(var.device		,   var.dtype.base_dtype		,   a_						)
			lowerCAmelCase  :     Dict       						= self._decay_weights_op(a_		,   a_		,   a_						)
			with tf.control_dependencies([decay]						):
					return super(a_		,   self						)._resource_apply_dense(a_		,   a_		,   **a_						)



	def 	_lowerCamelCase     ( self		,   a_		,   a_		,   a_		,   a_=None						):
			lowerCAmelCase						,		lowerCAmelCase  :     List[str]       						= self._get_lr(var.device		,   var.dtype.base_dtype		,   a_						)
			lowerCAmelCase  :     Optional[Any]       						= self._decay_weights_op(a_		,   a_		,   a_						)
			with tf.control_dependencies([decay]						):
					return super(a_		,   self						)._resource_apply_sparse(a_		,   a_		,   a_		,   **a_						)



	def 	_lowerCamelCase     ( self						):
			lowerCAmelCase  :     Union[str, Any]       						= super().get_config()
			config.update({"weight_decay_rate": self.weight_decay_rate}						)
			return config





	def 	_lowerCamelCase     ( self		,   a_						):
			if self.weight_decay_rate == 0:
					return False

			if self._include_in_weight_decay:
					for r in self._include_in_weight_decay:
							if re.search(a_		,   a_						) is not None:
									return True

			if self._exclude_from_weight_decay:
					for r in self._exclude_from_weight_decay:
							if re.search(a_		,   a_						) is not None:
									return False
			return True






class 		lowerCamelCase	(   _A							):



	def __init__( self						):
			lowerCAmelCase  :     Tuple       						= []
			lowerCAmelCase  :     Dict       						= None



	@property
	def 	_lowerCamelCase     ( self						):
			if self._accum_steps is None:
					lowerCAmelCase  :     Dict       						= tf.Variable(
					    tf.constant(0		,   dtype=tf.intaa						)		,   trainable=a_		,   synchronization=tf.VariableSynchronization.ON_READ		,   aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA		,   )

			return self._accum_steps.value()



	@property
	def 	_lowerCamelCase     ( self						):
			if not self._gradients:
					raise ValueError("The accumulator should be called first to initialize the gradients"						)
			return [gradient.value() if gradient is not None else gradient for gradient in self._gradients]



	def __call__( self		,   a_						):
			if not self._gradients:
					lowerCAmelCase  :     Tuple       						= self.step  # Create the step variable.
					self._gradients.extend(
					    [
					        tf.Variable(
					            tf.zeros_like(a_						)		,   trainable=a_		,   synchronization=tf.VariableSynchronization.ON_READ		,   aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA		,   )
					        if gradient is not None
					        else gradient
					        for gradient in gradients
					    ]						)
			if len(a_						) != len(self._gradients						):
					raise ValueError(F'''Expected {len(self._gradients						)} gradients, but got {len(a_						)}'''						)

			for accum_gradient, gradient in zip(self._gradients		,   a_						):
					if accum_gradient is not None and gradient is not None:
							accum_gradient.assign_add(a_						)

			self._accum_steps.assign_add(1						)





	def 	_lowerCamelCase     ( self						):
			if not self._gradients:
					return
			self._accum_steps.assign(0						)
			for gradient in self._gradients:
					if gradient is not None:
							gradient.assign(tf.zeros_like(a_						)						)










'''simple docstring'''






from __future__ import annotations

lowerCAmelCase									=   []






def   __A    (				a_    :	list[list[int]]   ,a_    :	int   ,a_    :	int						):
		for i in range(len(a_						)						):
				if board[row][i] == 1:
						return False
		for i in range(len(a_						)						):
				if board[i][column] == 1:
						return False
		for i, j in zip(range(a_   ,-1   ,-1						)   ,range(a_   ,-1   ,-1						)						):
				if board[i][j] == 1:
						return False
		for i, j in zip(range(a_   ,-1   ,-1						)   ,range(a_   ,len(a_						)						)						):
				if board[i][j] == 1:
						return False
		return True






def   __A    (				a_    :	list[list[int]]   ,a_    :	int						):
		if row >= len(a_						):
				solution.append(a_						)
				printboard(a_						)
				print()
				return True
		for i in range(len(a_						)						):
				if is_safe(a_   ,a_   ,a_						):
						lowerCAmelCase  :     Dict       						= 1
						solve(a_   ,row + 1						)
						lowerCAmelCase  :     Optional[int]       						= 0
		return False






def   __A    (				a_    :	list[list[int]]						):
		for i in range(len(a_						)						):
				for j in range(len(a_						)						):
						if board[i][j] == 1:
								print("Q"   ,end=" "						)
						else:
								print("."   ,end=" "						)
				print()


# n=int(input("The no. of queens"))
lowerCAmelCase									=   8
lowerCAmelCase									=   [[0 for i in range(n)] for j in range(n)]
solve(board, 0)

print("""The total no. of solutions are :""", len(solution))



